In this thesis, we introduce a signal-to-noise ratio (SNR) estimator and analyze the performance degradation of the SNR estimator due to the synchronization error in the orthogonal frequency division multiplexing (OFDM) systems. This SNR estimator through the expectation-maximization (EM) algorithm is used in the adaptive modulation. When the synchronization is imperfectly done, the synchronization error reduces the performance of the OFDM systems and the accuracy of the SNR estimator. We investigate the estimation offset of the SNR estimator with the synchronization error. Simulation results demonstrate that the theoretical analyses are correct. In addition, the simulation results show that the more synchronization errors cause the more estimation errors of the SNR estimator. And the estimation errors are not decreased by the iteration of the EM algorithm.

The bid-ask spread costs consist of three components, which include order processing costs, inventory-holding costs, and adverse selection costs. In this paper, we model the inventory-holding costs of the bid-ask spread by option hedging. Theinventory-holding costs are hedged by call or put option positions. Since trades deal with the adverse selection traders are unobservable. We treat it as a latent variable, and Expected-Maximization (EM) algorithm are applied to estimate the related parameters of the model. Simulation studies are performed for several different models. Empirical results of NYSE high frequency data show that the proposed model are obtain appropriate parameter estimation when the returns satisfied normality assumption.

This dissertation investigates three topics related to imagereconstruction from list-mode Anger camera data. Our mainfocus is the processing of photomultiplier-tube (PMT)signals directly into images. First we look at the use of list-mode calibration data toreconstruct a non-parametric likelihood model relating theobject to the data list. The reconstructed model can thenbe combined with list-mode object data to produce amaximum-likelihood (ML) reconstruction, an approach we calldouble list-mode reconstruction. This trades off reducedprior assumptions about the properties of the imaging systemfor greatly increased processing time and increaseduncertainty in the reconstruction. Second we use the list-mode expectation-maximization (EM)algorithm to reconstruct planar projection images directlyfrom PMT data. Images reconstructed by EM are compared withimages produced using the faster and more common techniqueof first producing ML position estimates, then histogramingto form an image. A mathematical model of the human visualsystem, the channelized Hotelling observer, is used tocompare the reconstructions by performing the Rayleigh task,a traditional measure of resolution. EM is found to producehigher resolution images than the histogram approach,suggesting that information is lost during the positionestimation step. Finally we investigate which linear parameters of an objectare estimable, in other words may be estimated without biasfrom list-mode data. We extend the notion of a linearsystem operator, familiar from binned-mode systems, tolist-mode systems, and show the estimable parameters aredetermined by the range of the adjoint of the systemoperator. As in the binned-mode case, the list-modesensitivity functions define ``natural pixels'' with whichto reconstruct the object.

In telecommunication, the series of mobile network exceptions is a processwhich exhibits surges and bursts. The bursty part is usually caused by systemmalfunction. Additionally, the mobile network exceptions are often timedependent. A model that successfully captures these aspects will make troubleshootingmuch easier for system engineers. The Hidden Markov Model(HMM) is a good candidate as it provides a mechanism to capture both thetime dependency and the random occurrence of bursts. This thesis focuses onan application of the HMM to mobile network exceptions, with a case study ofEricsson’s Dropped Call data. For estimation purposes, two methods of maximumlikelihood estimation for HMM, namely, EM algorithm and stochasticEM algorithm, are used.

Abstract In this thesis, iterative detection and estimation algorithms for digital communications systems in the presence of parametric uncertainty are explored and further developed. In particular, variational methods, which have been extensively applied in other research fields such as artificial intelligence and machine learning, are introduced and systematically used in deriving approximations to the optimal receivers in various channel conditions. The key idea behind the variational methods is to transform the problem of interest into an optimization problem via an introduction of extra degrees of freedom known as variational parameters. This is done so that, for fixed values of the free parameters, the transformed problem has a simple solution, solving approximately the original problem. The thesis contributes to the state of the art of advanced receiver design in a number of ways. These include the development of new theoretical and conceptual viewpoints of iterative turbo-processing receivers as well as a new set of practical joint estimation and detection algorithms. Central to the theoretical studies is to show that many of the known low-complexity turbo receivers, such as linear minimum mean square error (MMSE) soft-input soft-output (SISO) equalizers and demodulators that are based on the Bayesian expectation-maximization (BEM) algorithm, can be formulated as solutions to the variational optimization problem. This new approach not only provides new insights into the current designs and structural properties of the relevant receivers, but also suggests some improvements on them. In addition, SISO detection in multipath fading channels is considered with the aim of obtaining a new class of low-complexity adaptive SISOs. As a result, a novel, unified method is proposed and applied in order to derive recursive versions of the classical Baum-Welch algorithm and its Bayesian counterpart, referred to as the BEM algorithm. These formulations are shown to yield computationally attractive soft decision-directed (SDD) channel estimators for both deterministic and Rayleigh fading intersymbol interference (ISI) channels. Next, by modeling the multipath fading channel as a complex bandpass autoregressive (AR) process, it is shown that the statistical parameters of radio channels, such as frequency offset, Doppler spread, and power-delay profile, can be conveniently extracted from the estimated AR parameters which, in turn, may be conveniently derived via an EM algorithm. Such a joint estimator for all relevant radio channel parameters has a number of virtues, particularly its capability to perform equally well in a variety of channel conditions. Lastly, adaptive iterative detection in the presence of phase uncertainty is investigated. As a result, novel iterative joint Bayesian estimation and symbol a posteriori probability (APP) computation algorithms, based on the variational Bayesian method, are proposed for both constant-phase channel models and dynamic phase models, and their performance is evaluated via computer simulations.

Clustering is the process of finding underlying group structure in data. As the scale of data collection continues to grow, this “big data” phenomenon results in more complex data structures. These data structures are not always compatible with traditional clustering methods, making their use problematic. This thesis presents methodology for analyzing samples of four-way and higher data, examples of these more complex data types. These data structures consist of samples of continuous data arranged in multidimensional arrays. A large emphasis is placed on clustering this data using mixture models that leverage tensor-variate distributions to model the data. Parameter estimation for all these methods are based on the expectation-maximization algorithm. Both simulated and real data are used for illustration. / Thesis / Doctor of Science (PhD)

In this thesis, I am interested in estimating the difference between dependent proportions from a 2 × 2 contingency table when there are missing data. The Expectation-Maximization (EM) algorithm is used to obtain an estimate for the difference between correlated proportions. To obtain the standard error of this difference I employ a resampling technique known as bootstrapping. The performance of the bootstrap standard error is evaluated for different sample sizes and different fractions of missing information. Finally, a 100(1-α)% bootstrap confidence interval is proposed and its coverage is evaluated through simulation.

Model-based clustering is the use of finite mixture models to identify underlying group structures in data. Estimating parameters for mixture models is notoriously difficult, with the expectation-maximization (EM) algorithm being the predominant method. An alternative approach is the evolutionary algorithm (EA) which emulates natural selection on a population of candidate solutions. By leveraging a fitness function and genetic operators like crossover and mutation, EAs offer a distinct way to search the likelihood surface. EAs have been developed for model-based clustering in the multivariate setting; however, there is a growing interest in matrix-variate distributions for three-way data applications. In this context, we propose an EA for finite mixtures of matrix-variate distributions. / Thesis / Master of Science (MSc)

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Master of Science / Department of Statistics / Weixin Yao / Mixtures of factor analyzers have been popularly used to cluster the high dimensional data. However, the traditional estimation method is based on the normality assumptions of random terms and thus is sensitive to outliers. In this article, we introduce a robust estimation procedure of mixtures of factor analyzers using the trimmed likelihood estimator (TLE). We use a simulation study and a real data application to demonstrate the robustness of the trimmed estimation procedure and compare it with the traditional normality based maximum likelihood estimate.